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Donald Trump's lawyer is trying to silence adult-film star Stormy Daniels, obtaining a secret restraining order in a private arbitration proceeding and warning that she faces penalties if she publicly discusses a relationship with the president, NBC News has learned.

The new pressure on Daniels, whose real name is Stephanie Clifford, comes a day after she filed a lawsuit in a Los Angeles court alleging that a nondisclosure agreement she made to keep quiet about an "intimate" relationship with Trump is invalid because he never signed it.

Tuesday's lawsuit says that Trump attorney Michael Cohen — who brokered the agreement with Clifford during the presidential campaign — attempted to "intimidate" Clifford and "shut her up" by initiating what it calls a "bogus arbitration proceeding" against her in Los Angeles on Feb. 27, 2018.

Cohen and his attorney did not immediately respond to requests for comment from NBC News.